**Help Needed**
The picture below is a sketch of a picnic area with a courtyard. How much of the courtyard is available for use?

Problem 1

With simple interest, we take a percentage of the loan amount (or deposit depending how you frame things) to determine the interest paid or earned.

The simple interest formula is

i = P*r*t

Let's look at an example: You deposit $100 into an account earning 5% simple interest. You want to know how much interest you earn over 2 years.

i = P*r*t

i = 100*0.05*2

i = 10

You've earned $10 in simple interest. Notice how this is 10% of the original deposit ($100). You can think of the 5% interest rate doubling to 10% because we're working over a 2 year period.

---------------------------------

Compound interest is where we can't take a simple percentage of the deposit. This is because we must use this formula

A = P*(1+r/n)^(n*t)

variables are:

An example: You deposit $100 at an interest rate of 5%. The interest is compounded quarterly (4 times a year). How much interest have you made in 2 years?

The input values will be

So,

A = P*(1+r/n)^(n*t)

A = 100*(1+0.05/4)^(4*2)

A = 110.448610118141

A = 110.45

i = interest

i = A - P

i = 110.45 - 100

i = 10.45

You've made $10.45 in interest over the two year period.

As you can see, we used an exponential function to determine compound interest. Whereas with simple interest, the function was linear. Exponential functions grow much faster compared to linear functions.

======================================================

Problem 2

Savings accounts offer higher interest rates, which encourages people to save their money (hence the name). Checking accounts on the other hand are used to write checks and are there for immediate withdrawals of cash. Checking accounts are also used for debit cards, such as for online shopping.

Both types of accounts are useful in their own different ways. Linking them together is handy to quickly move money without having to deal with tons of paperwork and/or lots of time spent.

======================================================

Problem 3

APR = annual percentage rate

APY = annual percentage yield

The APR value is often the stated item on a loan, since it is the smaller of the two values. When it comes to savings accounts in banks, they tend to state the APY value since it is larger.

Let's look at an example:

The APR is 5% and the money is compounded monthly (12 times a year). Compute the APY.

----------

Solution:

The formula we use is

y = (1+r/n)^n

where y is the APY and r is the APR

In this case we have

Giving us the following

y = (1+r/n)^n - 1

y = (1+0.05/12)^12 - 1

y = 1.05116189788173 - 1

y = 0.0512

Then multiply that by 100, aka move the decimal point two spots to the right, to arrive at an APY of approximately 5.12%

This example demonstrates how compound interest slightly bumps up the amount of return. We've gone from 5.00% to 5.12%

This slight increase is because the money is compounded 12 times a year. Each time we compound, we're adding to the pile ever so slightly. There's a limit to this process (see the continuous compounding interest formula); i.e. we can't grow the APY forever.

If we were using simple interest, then the APY formula shown above would not apply. For simple interest situations, the APY and APR are the same value.

Answer:

Step-by-step explanation: There are three possible solutions for a linear equation: no solution, one unique solution, and infinitely many solutions.

A linear equation is an algebraic equation in which the highest exponent of the variables is 1. For example, 2x + 3 = 5 is a linear equation because the highest exponent of the variable x is 1.

If a linear equation has no solutions, this means that the equation is contradictory and there is no possible value of the variable that can make the equation true. For example, the equation 2x + 3 = 5 has no solutions because it is already true for all possible values of x.

If a linear equation has a unique solution, this means that there is only one possible value of the variable that can make the equation true. For example, the equation 2x + 3 = 5 has a unique solution because there is only one value of x that can make the equation true (in this case, x = 1).

If a linear equation has infinitely many solutions, this means that there are an infinite number of possible values of the variable that can make the equation true. This typically happens when the equation has the form of 0 = 0, which is always true for any value of the variable. For example, the equation 0 = 0 has infinitely many solutions because it is true for all possible values of x.

In general, you can tell whether a linear equation has no solutions, a unique solution, or infinitely many solutions by solving the equation. Solving a linear equation involves isolating the variable on one side of the equation and then using algebraic techniques to find its value. If you are able to find a unique value for the variable, then the equation has a unique solution. If you are unable to find a unique value for the variable, then the equation either has no solutions or infinitely many solutions.

Lower estimate obtained would be = 35.4 liters

Upper estimate obtained would be = 35.4 liters

What is Estimate?

Estimation finds an estimate or approximation.

An approximation is a value, amount, or size closest to the true value found by rounding off.

To find upper and lower estimates for the total quantity of erupted materials after six seconds using six equal subintervals, we can use the left endpoints and the right endpoints of the subintervals to find the estimates.

The lower estimate is obtained by using the left endpoints of the subintervals to estimate the value of r(t) at each subinterval. Since there are six subintervals, we have:

lower estimate = (28 + 18 + 34 + 48 + 54 + 60) * (6/6) = 324 tons

The upper estimate is obtained by using the right endpoints of the subintervals to estimate the value of r(t) at each subinterval. We have:

upper estimate = (18 + 34 + 48 + 54 + 60 + 60) * (6/6) = 324 tons

To use the midpoint rule to estimate Q(6) using three equal subintervals, we need to find the midpoints of the subintervals. The subintervals are [0,2], [2,4], and [4,6]. The midpoints are 1, 3, and 5. The value of r(t) at these points is 18, 48, and 54 respectively. The midpoint rule estimate is given by:

Q(6) = (18 + 48 + 54) * (6/3) = 180 tons

To find lower and upper estimates for the total amount of oil leaked over the interval [0, 10] using five equal subintervals, we can again use the left endpoints and the right endpoints of the subintervals to find the estimates. The lower estimate is obtained by using the left endpoints of the subintervals to estimate the value of r(t) at each subinterval. The upper estimate is obtained by using the right endpoints of the subintervals to estimate the value of r(t) at each subinterval.

The subintervals are [0,2], [2,4], [4,6], [6,8], and [8,10]. The left endpoints are 0, 2, 4, 6, and 8, and the right endpoints are 2, 4, 6, 8, and 10. The lower estimate is obtained by using the left endpoints:

lower estimate = (8.6 + 7.5 + 6.7 + 6.4 + 5.7) * (10/5) = 35.4 liters

The upper estimate is obtained by using the right endpoints:

upper estimate = (7.5 + 6.7 + 6.4 + 5.7 + 5.1) * (10/5) = 35.4 liters

Hence, The Lower estimate obtained would be = 35.4 liters and

Upper estimate obtained would be = 35.4 liters

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The expression that represents the length of Ana Maria's ribbon is r/3

A word problem is a mathematical exercise where significant background information on the problem is presented in ordinary language rather than in mathematical notation. It should be noted that an expression shows the relationship between the variables.

Ana Maria has the length of 1/3 ribbon Jolie has.

Let r represent the length of ribbon Jolie has

Since Ana Maria's ribbon length is 1/3 that of Jolie ribbon. We can write:

Ana Maria's ribbon length = 1/3 × r = r/3

Thus, the expression for Ana Maria's ribbon length is r/3.

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The expression that represents the length of Ana Maria's ribbon is r/3

How to determine which expression can be used to represent the length?

A word problem is a mathematical exercise where significant background information on the problem is presented in ordinary language rather than in mathematical notation. It should be noted that an expression shows the relationship between the variables.

Ana Maria has the length of 1/3 ribbon Jolie has.

Let r represent the length of ribbon Jolie has

Since Ana Maria's ribbon length is 1/3 that of Jolie ribbon. We can write:

Ana Maria's ribbon length = 1/3 × r = r/3

Thus, the expression for Ana Maria's ribbon length is r/3. :)

a. Constant speed, C =  0. 19 miles/minutes

b. The fraction representing her constant speed is  1/x miles/minutes

c. The time it takes her to drive exactly 1 mile is 5. 38 minutes

The formula for calculating constant speed is expressed as;

Constant speed = total distance covered/ total time taken

From the information given, we have that;

Now, substitute the values into the formula

Constant speed = 1. 3 / 7

Divide the values

Constant speed = 0. 19 miles/minutes

When distance 1 mile, time taken = x minutes

Constant speed = 1/x miles/minutes

If 1. 3 miles = 7 minutes

Then, 1 mile = x

cross multiply

x = 7/1. 3

x = 5. 38 minutes

Hence, the constant speed is 0. 19 miles/minutes

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Answer:

--------------------------------

Find the following:

Answer:

[tex]h(-3)=\boxed{\dfrac{5}{4}}[/tex]

[tex]h(2)=\boxed{3}[/tex]

[tex]h(5)=\boxed{-\dfrac{19}{4}}[/tex]

Step-by-step explanation:

Given piecewise function:

[tex]h(x) \begin{cases} -\dfrac{3}{4}x-1\; &\text{if}\;x\neq 2\\\\3 \; &\text{if}\;x=2 \end{cases}[/tex]

To find h(-3), substitute x = -3 into the function:

[tex]\begin{aligned}\implies h(-3)&=-\dfrac{3}{4}(-3)-1\\\\&=\dfrac{9}{4}-1\\\\&=\dfrac{9}{4}-\dfrac{4}{4}\\\\&=\dfrac{5}{4}\end{aligned}[/tex]

To find h(2), substitute x = 2 into the function:

[tex]\implies h(2)=3[/tex]

To find h(5), substitute x = 5 into the function:

[tex]\begin{aligned}\implies h(5)&=-\dfrac{3}{4}(5)-1\\\\&=-\dfrac{15}{4}-1\\\\&=-\dfrac{15}{4}-\dfrac{4}{4}\\\\&=-\dfrac{19}{4}\end{aligned}[/tex]

The integral [tex]\int\limits^a_b {I (t)} \, dt[/tex]represents the total change in the charge from time t= b to t = a. Or in other words, it is the total amount of charge passed through between t = a and t = b.

The ultimate value of a quantity, according to the net change theorem, equals the beginning value plus the integral of the rate of change when a quantity changes. Net change can be either a positive, negative, or zero number.

The Net Change Theorem: The integral of a rate of change is the net change.

[tex]\int\limits^a_b {F'(x)} \, dx[/tex]  = F(b) − F(a)

[tex]\int\limits^a_b {I (t)} \, dt[/tex] &  I(t) = Q'(t)

Consider the given integral,

[tex]\int\limits^a_b {I (t)} \, dt[/tex], where I(t) = Q'(t)

Now substitute the value  I(t) = Q'(t) in  [tex]\int\limits^a_b {I (t)} \, dt[/tex]. It becomes[tex]\int\limits^a_b {I (t)} \, dt[/tex] = [tex]\int\limits^a_b[/tex]Q'(t) by using the Net Change Theorem,

[tex]\int\limits^a_b[/tex] Q'(t) dt = Q(b)−Q(a)  

[tex]\int\limits^a_b {I (t)} \, dt[/tex] = Q(b)−Q(a)

The integral [tex]\int\limits^a_b {I (t)} \, dt[/tex] represents the change in the charge from time b to a.

Therefore, [tex]\int\limits^a_b {I (t)} \, dt[/tex] represents the change in the charge from time t= b to t= a.

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The Perimeter of the Quadrilateral will be P = 3s³ + s² + 5s + 1

What is Quadrilateral?

A quadrilateral is a four-sided polygon with four edges and four corners in geometry. The name derives from the Latin words quadri (a variation of four) and latus (a side).

Solution:

Given:

Length of Longest side is three times more than the cube of shortest side

Length of Another side is 6cm less than square of shortest side

Length of Third side is 7cm more than four times the length of shortest side

To Find:

Perimeter of the Quadrilateral in terms of Shortest Side

Let, Shortest Side be s

So, longest side will be 3 * s³

Another Side will be s² - 6

Third Side will be 4s + 7

Perimeter of the Quadrilateral will be s + 4s +7 + s² - 6 + 3s³

5s + 1 + s² + 3s³

P = 3s³ + s² + 5s + 1

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When you start from the given set of rules and conditions and determine must be true you are using c) Deductive reasoning.

In deductive reasoning, conclusions are reached based on premises that are typically taken to be true. It employs a logical premise to arrive at a logical conclusion and is also known as "deductive logic." The term "top-down reasoning" is frequently used to describe deductive reasoning. If something is presumptively true and a different object is connected to the first presumption, then the original truth must also apply to the second. Syllogism is one of the most popular forms of deductive reasoning. A major and a minor assertion coming together to make a logical conclusion is referred to as a syllogism. The fact that the two statements are true indicates that the assertion will probably be true for all further premises belonging to that category.

Given,

When you start from the given set of rules and conditions and determine must be true you are using ___ reason.

c) Deductive reasoning

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No, these two triangles are not congruent. Congruent triangles have the same shape and size, and Triangle ABC and Triangle DEF do not have the same shape or size.

Congruent triangles are two triangles that have the same shape and size. This means that the angles and the side lengths of the two triangles must be the same. For example, if two triangles have three angles that measure 60°, 60°, and 60°, the two triangles are congruent. Similarly, if two triangles have three side lengths of 5 cm, 6 cm, and 7 cm, the two triangles are also congruent. However, Triangle ABC and Triangle DEF do not have the same shape or size, therefore, they are not congruent. The angles and side lengths of the two triangles are not the same, so they cannot be congruent.

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the complete question is

determine whether each pair of triangles is congruent. if so, write a congruence statement and explain why the triangles are congruent.

Triangle ABC and Triangle DEF

Answer:

C

Step-by-step explanation:

slope of the first line =  -9/2

slope of a perpendicular line = 2/9

y-(-1)= 2/9(x-0)

y + 1 = 2/9 x

y = 2/9 x -1

The grand mean fir the observations of the age of three different types of vehicles currently on the road: trucks, cars, and vans is Eight . So, correct option is option B.

The overall or pooled average is the average of multiple subsample averages, as long as the subsamples have the same number of data points. In ANOVA, the overall mean for a set of multiple subsamples is the mean of all observations. that is, each data point divided by the common sample size.

∑x = represented by the sum of the averages of all sets. Overall grand mean formula is

Grand mean = sum of all sample mean / total number of sentences

We have given that,

Autotrader would like to test difference exists in the age of three different types of vehicles.

let set A , set B and set C represents the ages of three different vichles i.e trunks , cars and vans respectively.

From table we get,

Mean of ages of trunks , A = 10

Mean of ages of cars , B = 8

Mean of ages of vans , C = 6

Grand mean = (10+8+6)/3 = 8

Hence, the grand mean is 8..

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The rounding of 46,650 to the nearest million is given as follows:

0.

To round a number, the number at the next place relative to the rounding place must be looked:

Examples of rounding to the nearest tenth are given as follows:

The numbers to the nearest million are rounded according to the example given as follows:

For this problem, we are given a number that is less than 500,000, hence the rounding of the number to the nearest million is of 0.

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Answer:

see explanation

Step-by-step explanation:

y = - x² + 4

can be expressed in functional notation as

f(x) = - x² + 4

to find the range value, substitute the domain value into f(x) , that is

f(3) = - 3² + 4 = - 9 + 4 = - 5

range value is then - 5

Answer:

X = -2 - 2(square root)3 or x = -2 + 2 (square root )3

Step-by-step explanation:

Answer:

The time when the rocket is at its highest point is 8.5 seconds.

The the equation of line in slope - intercept form is [tex]y = -\frac{1}{3}x-3[/tex] and the slope for the given table is 0.

What is slope intercept form of the line?

When you know the slope of the line to be examined and the given point is also the y intercept, you can use the slope intercept formula, y = mx + b. (0, b). The y value of the y intercept point is denoted by the symbol b in the formula.

Given:

The line passes through the point (3, -4) and having the slope is -1/3.

Consider the point - slope form of the line,

[tex]y-y_1=m(x-x_1)[/tex]

where, [tex](x_1, x_2)[/tex] is the given point and m is the slope.

Plug [tex](x_1, y_1) = (3, -4)[/tex] and m = -1/3 in the above equation.

[tex]y-(-4)=-\frac{1}{3}(x-3)\\ y+4=-\frac{1}{3}x+1\\ y=-\frac{1}{3}x+1-4\\ y=-\frac{1}{3}x-3[/tex]

This is the equation of line in slope - intercept form.

Now to find the slope of the line that passes through the given points on the table.

Since,

Slope = [tex]\frac{Change In y}{Change In x}[/tex]

From the given table the change in y is 0, and the change in x is 5 for all the values.

So,

Slope = 0/5 = 0

Hence, the the equation of line in slope - intercept form is [tex]y = -\frac{1}{3}x-3[/tex] and the slope for the given table is 0.

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Step-by-step explanation:

an arithmetic operation (like "-") on functions is the same as using the same operation on the functional excursions themselves.

(f - g)(x) = -x + 3 - (-10x - 9) = -x + 3 + 10x + 9 =

= 9x + 12

(f - g)(8.5) = 9×8.5 + 12 = 76.5 + 12 = 88.5

The rate of growth in the exponential function is 1.98%

An exponential function is defined by the formula f(x) = aˣ, where the input variable x occurs as an exponent. The exponential curve depends on the exponential function and it depends on the value of the x.

To solve this problem, we have to model the growth in an exponential function.

Population in 1997 = 2.12 million

Population in 2006 = 2.53 million

Time = 9

Since this is an exponential growth function, we can write this as;

2.53 = 2.12(1 + r)⁹

where r = rate of growth

2.53 = 2.12(1 + r)⁹

r = 0.0198

r = 1.98%

The rate of growth is 1.98%

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By using distance formula, it can be calculated that

Length of the rectangle is 4 units

Width of the rectangle is 2 units

Perimeter of the rectangle is 12 units

Area of the rectangle = 8 sq. units

Distance between (0, 0) and (4, 0) = [tex]\sqrt{(4-0)^2 + (0 - 0)^2}[/tex]

                                                         = [tex]\sqrt{16}[/tex]

                                                         = 4 units

Length of the rectangle is 4 units

Distance between (0, 0) and (0, 2) = [tex]\sqrt{(0-0)^2 + (0 - 2)^2}[/tex]

                                                         = [tex]\sqrt{4}[/tex]

                                                         = 2 units

Width of the rectangle is 2 units

Perimeter of the rectangle = 2 [tex]\times[/tex] (4  +2)

                                            = 12 units

Area of the rectangle = 4 [tex]\times[/tex] 2 = 8 sq. units

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The "winning" guess when  played this game has been around 18.

The quality of being guided by or based on reasons is referred to as rationality. In this sense, a belief is rational if it is based on strong evidence, and an individual acts rationally if they have a good reason for doing so. This quality can be applied to a skill, like reasoning in a rational animal, a psychological process, like reasoning, mental states, like beliefs and intentions, or people who have these other kinds of rationality. If something does not meet the standards of rational evaluation, it is either irrational or rational, depending on where it falls outside the realm of rational evaluation.

Given you have to choose a number between 0 and 100. the winner of the game is the person whose number is closest to 2/3 times the average of all chosen numbers,

Theoretically,  concur that the answer is 0. As stated, this is due to widespread rationality knowledge. You should guess 2/3*50=33 if everyone chose equally between 0 and 100. The average would be 50. Everyone ought to guess 33 if they are all aware of this. However, if I know that everyone correctly predicted 33, then 33 is the average, and should seek 2/3*33=22. This logic continues until everyone should correctly guess 0.

People actually don't think this way, but I disagree that you should guess between 5 and 10, which I believe is too low. depending on who you play with, as a group of game theorists might get a lower average than a group of people from the average population.) In a real-world setting, you need to consider how many iterations the others will make. You should guess 22 if you think they will only do one, which would result in everyone guessing 33. If you assume that they iterate the reasoning twice on average and guess 22, you should estimate 15 and so on.

The "winning" guess when  played this game has been around 18.

Hence the guess should be 18.

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the complete question is,

Several people choose an integer between 0 and 100. The winner is the person whose integer is closest to 2/3 of the average of the numbers reported by all seven participants. What value would you choose?

The triangles are considered to be congruent if one right triangle's hypotenuse and another right triangle's hypotenuse are equal.

Given, assuming that the hypotenuse of one right triangle is equivalent to the hypotenuse of another right triangle, then the triangles are harmonious.

The given statement must be verified as true or false by us.

According to the RHS congruence theorem, two right-angled triangles are congruent if the hypotenuse and side of one triangle are equal to the hypotenuse and side of another.

The hypotenuse and the side of the triangle that corresponds to it must be equal according to the RHS rule.

The hypotenuses of the two triangles are equal, per the question.

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The points is a solution for this inequality is (0, -3).

What is inequality?

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign (≠)" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.

Switch sides

[tex]\frac{2}{3} x+1 \geq y$$[/tex]

Move 1 to the right side

[tex]\frac{2}{3} x \geq y-1$$[/tex]

Multiply both sides by 3

[tex]3 \cdot \frac{2}{3} x \geq 3 y-3 \cdot 1$$[/tex]

Simplify

[tex]2 x \geq 3 y-3$$[/tex]

Divide both sides by 2

[tex]\frac{2 x}{2} \geq \frac{3 y}{2}-\frac{3}{2}$$[/tex]

Simplify

[tex]x \geq \frac{3 y-3}{2}$$[/tex]

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In order to enclose the garden's perimeter, vintage fence will be used. The perimeter of a rectangle-shaped garden is equal to the sum of the garden's two lengths and two widths.

In order to enclose the garden's perimeter, vintage fence will be used. The perimeter of a rectangle-shaped garden is equal to the sum of the garden's two lengths and two widths.

According to their estimates, our perimeter fence measures 220 feet, hence 220 = 2L + 2W.

We can make this more manageable if we divide everything by two: 110 = L + W

The width is now specified as being "exactly two-thirds of the length."

In math, the letter "=" equals the word "IS". Consequently, "the width is" becomes "W =," and "the two-thirds of the length" is precisely what it says, "(2/3) L."

W = (2/3)L is the result of adding these.

and we will add this W to the formula above (110 = L + W) to make 110 = L + (2/3)L.

If we substitute L with (3/3) L (that is, 1*L with 1 written 3/3) now we can add (3/3) as adding fractions requires a "common denominator."

L + (2/3)

L = (5/3)L

At this point, our equation is 110 = (5/3)L.

The right side (3/5) is now multiplied by the reciprocal on both sides, yielding (3/5)(110) = (3/5)(5/3)

L66 = L and W=2/3

L = (2/3)(66) = 44 = W

66 feet by 44 feet are the measurements of the square flower garden.

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Chris's time 3.058 sec faster than Michael's.

What is meaning of faster?

Fast and fast refer to moving quickly. Fast can be used as an adverb or an adjective. Quick is an adjective, while rapidly is its adverbial counterpart.

Given that,

Chris completed a 100-meter breaststroke swimming race in 92.542 seconds.

Michael completed the 100-meter breaststroke swimming race in 95.6 seconds.

The difference of time between Chris and Michael to complete 100-meter breaststroke swimming is = (95.6 - 92.542) = 3.058 sec.

Since both are completed 100 meter breaststroke, thus the difference of time denotes the faster time.

Thus Michael's timing was 3.058 seconds slower than Chris'.  

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The time left before the fossil fuel reserves run out is 2000years(1significant figure)

A rate is a special ratio in which the two terms are in different units. For example, if a 14-ounce can of corn costs 69¢, the rate is 69¢ for 14 ounces. Rate can also be defined as the ratio of two unlike units.

The total metric tonnes of fossil fuel on earth is 2.1×10⁸.

The rate of usage is 1×10⁵ metric tone of fossil fuel per year

as been said rate = total metric tone of fuel/ number of years to use

1×10⁵= 2.1×10⁸/no of years

no of years = 2.1×10⁸/1×10⁵

no of years = 2.1×10³years= 2100years

to 1 significant figure = 2000years

therefore the number of years for the fossil fuel to run out is 2000years

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Answer: x = 8 1/2 i believe

Step-by-step explanation:

whats the question im getting off camera blind explain it to me

Answer:

Step-by-step explanation:

m = slope

m =  (-7 -3 ) / (4 -(-1)

m = -10 / 5

m = -2

ask, if you want to understand  how I got that.  :)